Abstract
Travel time variability (TTV) must be considered in evaluations of the effect of traffic control on transport network performance. The objective of this paper was to investigate the relationship between a travel time variability diagram (TTVD), which relates average travel time to its standard deviation, and a macroscopic fundamental diagram (MFD), which relates average network flow to its average density. Recent studies indicated hysteresis loops in TTVD (for journeys with the same average travel time, the TTVs for departures as congestion dissipates are higher than the TTVs for departures during congestion onset) and in the MFD (with the same network density, higher network flows occur during congestion onset than during congestion offset). Based on a simulation results, we evaluated the correlations between these loops in a multimodal network. Strong correlations were found between TTVD and MFD loops. Next, we developed combined diagrams of travel time standard deviations against network flow and density. These diagrams revealed the presence of a critical network flow and density during congested periods; beyond these critical points, the TTV increases sharply. These findings may facilitate evaluation of management strategies that consider both traffic flow and reliability measures.
Similar content being viewed by others
References
Lyman, K., Bertini, R.: Using travel time reliability measures to improve regional transportation planning and operations. Transp. Res. Rec. J. Transp. Res Board. 2046, 1–10 (2008). https://doi.org/10.3141/2046-01
Saberi, M., Bertini, B.: “Beyond Corridor Reliability Measures: Analysis of Freeway Travel Time Reliability at the Segment Level for Hot Spot Identification” in Transportation Research Board 89th Annual Meeting. Washington, DC (2010)
Hasan, S., Ben-Akiva, M.E., Choudhury, C., Emmonds, A.: Modeling travel time variability on urban links in London. In: Proceedings of European Transport Conference, the Netherlands (2009)
Rakha, H, El-Shawarby, I, Arafeh, M and Dion, F, “Estimating path travel-time reliability” in proceedings of 9th international IEEE conference on intelligent transportation systems, Toronto, 2006, pp. 236–241
Geroliminis, N., Daganzo, C.: Existence of urban-scale macroscopic fundamental diagrams: some experimental findings. Transp. Res. B Methodol. 42(9), 759–770 (2008). https://doi.org/10.1016/j.trb.2008.02.002
Buisson, C., Ladier, C.: Exploring the impact of homogeneity of traffic measurements on the existence of macroscopic fundamental diagrams. Transp. Res. Rec. J. Transp Res. Board. 2124, 127–136 (2009). https://doi.org/10.3141/2124-12
Ji, Y., Daamen, W., Hoogendoorn, S., Hoogendoorn-Lanser, S., Qian, X.: Investigating the shape of the macroscopic fundamental diagram using simulation data. Transp. Res. Rec. J Transp. Res. Board. 2161, 40–48 (2010). https://doi.org/10.3141/2161-05
Mahmassani, H., Hou, T., Saberi, M.: Connecting networkwide travel time reliability and the network fundamental diagram of traffic flow. Transp. Res. Rec. J. Transp. Res. Board. 2391, 80–91 (2013). https://doi.org/10.3141/2391-08
Bates, J., Fearon, J., Black, I.: Frameworks for modelling the variability of journey times on the highway network. In: Technical Report, ARUP (2004)
Mazloumian, A, Geroliminis, N and Helbing, D, “The spatial variability of vehicle densities as determinant of urban network capacity”, philosophical transactions of the Royal Society a: mathematical, physical and engineering sciences, 368(1928), 2010, pp. 4627-4647, https://doi.org/10.1098/rsta.2010.0099
Geroliminis, N., Sun, J.: Properties of a well-defined macroscopic fundamental diagram for urban traffic. Transp. Res. B Methodol. 45(3), 605–617 (2011). https://doi.org/10.1016/j.trb.2010.11.004
Mittal, A., Mahmassani, H., Talebpour, A.: Network flow relations and travel time reliability in a connected environment. Transp. Res. Rec. J. Transp. Res. Board. 2622, 24–37 (2017). https://doi.org/10.3141/2622-03
Yildirimoglu, M., Koymans, A., Geroliminis, N.: “Exploring the Properties of Mean-Variance Relations in Freeway Travel Times” in Transportation Research Board 92nd Annual Meeting. Washington, DC (2013)
Gayah, V., Dixit, V., Guler, S.: Relationship between mean and day-to-day variation in travel time in urban networks. EURO J Transp. Logist. 3(3-4), 227–243 (2013). https://doi.org/10.1007/s13676-013-0032-2
Van Lint, J., van Zuylen, H., Tu, H.: Travel time unreliability on freeways: why measures based on variance tell only half the story. Transp. Res. A Policy Pract. 42(1), 258–277 (2008). https://doi.org/10.1016/j.tra.2007.08.008
Brownstone, D., Small, K.: Valuing time and reliability: assessing the evidence from road pricing demonstrations. Transp. Res. A Policy Pract. 39(4), 279–293 (2005). https://doi.org/10.1016/j.tra.2004.11.001
Bates, J., Polak, J., Jones, P., Cook, A.: The valuation of reliability for personal travel. Transport Res E-Log. 37(2-3), 191–229 (2001). https://doi.org/10.1016/s1366-5545(00)00011-9
Lam, T., Small, K.: The value of time and reliability: measurement from a value pricing experiment. Transport Res E-Log. 37(2-3), 231–251 (2001). https://doi.org/10.1016/s1366-5545(00)00016-8
Wahaballa, A.M., Kurauchi, F., Takagi, A., Othman, A.M.: Benefits of improvement in travel time reliability resulting from real-time information provision. In: Proceedings of the 5th International Symposium on Transportation Network Reliability, Hong Kong (2012)
Wahaballa, A.M., Kurauchi, F., Takagi, A., Othman, A.M.: Review of benefit evaluation models for travel time reliability improvements. In: Proceedings of the 41st Conference on Infrastructure Planning, p. 2010. Japan Society of Civil Engineering, Nagoya
Prigogine, I., Herman, R.: Kinetic Theory of Vehicular Traffic. Elsevier, New York (1971)
Taylor, M.: Travel time variability—the case of two public modes. Transp. Sci. 16(4), 507–521 (1982). https://doi.org/10.1287/trsc.16.4.507
Mahmassani, H., Hou, T., Dong, J.: Characterizing travel time variability in vehicular traffic networks. Transp. Res. Rec. J. Transp. Res. Board. 2315, 141–152 (2012). https://doi.org/10.3141/2315-15
Saberi, M., Mahmassani, H.: Exploring properties of networkwide flow-density relations in a freeway network. Transp. Res. Rec. J. Transp. Res. Board. 2315, 153–163 (2012). https://doi.org/10.3141/2315-16
Knoop, V, Hoogendoorn, S and van Lint, J, “Routing strategies based on macroscopic fundamental diagram”, Transp. Res. Rec. J. Transp. Res. Board, 2315, 2012, pp. 1–10, https://doi.org/10.3141/2315-01
Zheng, N., Waraich, R., Axhausen, K., Geroliminis, N.: “A dynamic cordon pricing scheme combining the macroscopic fundamental diagram and an agent-based traffic model”, transportation research part a: policy and practice, 46(8), 2012, pp. 1291-1303. https://doi.org/10.1016/j.tra.2012.05.006
Zheng, N., Geroliminis, N.: On the distribution of urban road space for multimodal congested networks. Transp. Res. B Methodol. 57, 326–341 (2013). https://doi.org/10.1016/j.trb.2013.06.003
Fosgerau, M.: On the relation between the mean and variance of delay in dynamic queues with random capacity and demand. J. Econ. Dyn. Control. 34(4), 598–603 (2010). https://doi.org/10.1016/j.jedc.2009.12.002
Vickrey, W.: Congestion theory and transport investment. Am. Econ. Rev. 59(2), 251–260 (1969) http://www.jstor.org/stable/1823678
Gayah, V., Daganzo, C.: Clockwise hysteresis loops in the macroscopic fundamental diagram: an effect of network instability. Transp. Res. B Methodol. 45(4), 643–655 (2011). https://doi.org/10.1016/j.trb.2010.11.006
Edie, L.C.: Discussion of traffic stream measurements and definitions. In: Almond, J. (ed.) Proceedings of the 2nd International Symposium on the Theory of Traffic Flow, pp. 139–154. OECD, Paris (1963)
Treiterer, J., Myers, J.: “The hysteresis phenomenon in traffic flow” in proceedings of the 6th international symposium on transportation and traffic theory. ISTTT. 6, 13–38 (1974)
Zhang, H.: A mathematical theory of traffic hysteresis. Transp. Res. B Methodol. 33(1), 1–23 (1999). https://doi.org/10.1016/s0191-2615(98)00022-8
Nagel, K, and Flötteröd, G, “Agent-Based Traffic Assignment: Going from Trips to Behavioral Travelers” in Proceedings of the 12th International Conference on Travel Behaviour Research (IATBR), Jaipur, 2009
Chakirov, A., Fourie, P.: Enriched Sioux Falls scenario with dynamic and disaggregate demand. Arbeitsberichte Verkehrs-und Raumplanung. 978, 2014 (2014) http://hdl.handle.net/20.500.11850/80996
Rieser, M., Grether, D., Nagel, K.: Adding mode choice to multiagent transport simulation. Trans. Res. Rec. J. Transp. Res. Board. 2132, 50–58 (2009). https://doi.org/10.3141/2132-06
Hemdan, S., Wahaballa, A.M., Kurauchi, F.: Quantification of the hysteresis of macroscopic fundamental diagrams and its relationship with the congestion heterogeneity and performance of a multimodal network. J. Transp. Technol. 8(1), 44–64 (2018). https://doi.org/10.4236/jtts.2018.81003
Hemdan, S., Wahaballa, A.M., Kurauchi, F.: Evaluating travel choices effect on multimodal network performance using vehicle and passenger macroscopic fundamental diagrams. J East Asia Soc. Transp. Studies. 12, 1710–1727 (2017). https://doi.org/10.11175/easts.12.1710
Rieser, M.: Adding Transit to an Agent-Based Transportation Simulation. PhD dissertation, Swiss Federal Institute of Technology (2010)
Grether, D., Chen, Y., Rieser, M., Nagel, K.: “Effects of a Simple Mode Choice Model in a Large-Scale Agent-Based Transport Simulation”, in Advances in Spatial Science, pp. 167–186. Complexity and Spatial Networks, Springer Berlin Heidelberg (2009)
Horni, A, Charypar, D and Axhausen, K.W, “Variability in Transport Microsimulations Investigated for MATSim: Preliminary Results”, Eidgenössische Technische Hochschule Zürich, Institut für Verkehrsplanung und Transportsysteme, 2011
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hemdan, S., Wahaballa, A.M. & Kurauchi, F. Travel Time Variability and Macroscopic Fundamental Diagram Relationships in Multimodal Networks. Int. J. ITS Res. 17, 114–124 (2019). https://doi.org/10.1007/s13177-018-0161-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13177-018-0161-y